This paper analyses the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is defined as an indicator of the generic competence: Use of Technology. Additionally, we show that using CAS could help to enhance the following generic competences: Self Learning, Planning and Organization, Communication and Writing, Mathematical and Technical Writing, Information Management and Critical Thinking. A follow-up at several stages of the resolution of a problem-example shall be performed; analysing each contribution of Maxima to the competences' acquisition. The problem-example concerns an electronic device for a building surveillance system, with different possibilities according to the number of sides of the building and other parameters. (Contains 3 figures.)